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9 cubed, (9)3, is the number you get when multiplying 9 times 9 times 9.
It can also be looked at as exponentiation involving the base 9 and the exponent 3.
The term is usually pronounced 3rd power of nine or nine cubed.
The cube of 9 is a perfect cube because the number is the product of the three equal integers 9.
It can be written as 9 × 9 × 9 or in exponential form.
Read on to learn everything about the number nine cubed, including useful identities.
Calculator
9 × 9 × 9 = 729
The inverse operation of cubing 9 is extracting the cube root of 9, explained here.
In the next section we elaborate on the cube 9.
What is 9 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 9 has an area of 729.
The sum and the differences of two cubes, for example with side length 9 and 8, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 9, b = 8 and the equivalence we get:
(9)3 = 17 x (92 – 9 × 8 + 82) – 83 = 17 x (81 – 72 + 64) – 512 = 17 x 73 – 512 = 729 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 9, b = 8 and the equivalence we get:
(9)3 = (92 + 9 × 8 + 82) + 83 = 81 + 72 + 64 + 512 = 729
As follows from (1), 9 cubed can be calculated from 8 cubed and 9 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(9)3 = (2 × 9 – 1) × (92 – 9 + 1) – (8)3 = 17 × (81 – 8) – 512 = 17 × 73 – 512 = 729
Using the second formula 9 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(9)3 = 83 + 3 × 92 – 3 × 9 + 1 = 512 + 3 × 81 – 3 × 9 + 1 = 512 + 243 – 27 + 1 = 729
If you want to calculate the cube of any number, not only integers like 9, you can use our calculator above.
Just enter your number; nothing else to be done.
A cube similar to 9 is, for example: cube of 11.
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The following table contains the cubes of numbers close to 9.
Table
| Number | Cube |
|---|---|
| 4 | 64 |
| 5 | 125 |
| 6 | 216 |
| 7 | 343 |
| 8 | 512 |
| 9 | 729 |
| 10 | 1,000 |
| 11 | 1,331 |
| 12 | 1,728 |
| 13 | 2,197 |
| 14 | 2,744 |
Nine Cubed
You now know everything about the cube 9 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
9 cubed is equivalent to 729.
If you were searching for what is 9 cubed in math or if you typed whats 9 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube9, and 9 to the 3rd power, just to name a few more examples people are often looking for.
Note that you can also find many perfect cubes including 9 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
9 cubed = 9 x 9 x 9 = (9)3 = 9 to the 3rd power = 729.
The exponentiation form is mostly used to denote 9 cube.
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– Article written by Mark, last updated on November 26th, 2023